The constrained transport (CT) method reflects the state of the art numerical technique for preserving the divergence-free condition of magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or upwind, conservative codes. The evolution of the different magnetic field components, located at zone interfaces using a staggered representation, is achieved by calculating the electric field components at cell edges, in a way that has to be consistent with the Riemann solver used for the update of cell-centered fluid quantities at interfaces. Albeit several approaches have been undertaken, the purpose of this work is, on the one hand, to compare existing methods in terms of robustness and accuracy and, on the other, to extend the upwind contrained transport (UCT) method by Londrillo & Del Zanna (2004) and Del Zanna et al. (2007) for the systematic construction of new averaging schemes. In particular, we propose a general formula for the upwind fluxes of the induction equation which simply involves the information available from the base Riemann solver employed for the fluid part, provided it does not require full spectral decomposition, and 1D reconstructions of velocity and magnetic field components from nearby intercell faces to cell edges. Our results are presented here in the context of second-order schemes for classical MHD, but they can be easily generalized to higher than second order schemes, either based on finite volumes or finite differences, and to other physical systems retaining the same structure of the equations, such as that of relativistic or general relativistic MHD.

约束传输（CT）方法反映了在使用Godunov型或迎风型保守代码进行的多维MHD仿真中，为了保持磁场的无散度条件而保持机器的精度的最新数值技术。通过使用交错表示法，通过使用计算单元边缘处的电场分量，必须与用于更新以单元为中心的Riemann解算器一致，来实现使用交错表示位于区域界面处的不同磁场分量的演化。界面处的流体量。尽管已采取了几种方法，但这项工作的目的是一方面在鲁棒性和准确性方面比较现有方法，另一方面扩大上风禁忌运输的范围。（UCT）方法由Londrillo和Del Zanna（2004）和Del Zanna et al。（2007年）的新平均方案的系统建设。特别是，我们提出了感应方程上风通量的通用公式，该公式仅涉及流体部分所使用的基本黎曼求解器的可用信息，前提是该方法不需要全光谱分解以及速度和磁场的一维重建从附近单元格面到单元格边缘的分量。我们的结果是在经典MHD的二阶方案的背景下呈现的，但基于有限的体积或有限的差异，它们可以很容易地推广到高于二阶方案，并且可以推广到保留相同结构的其他物理系统。等式，例如相对论或广义相对论MHD。